This paper is motivated by the inverse tomography (or Calderón) problem for Riemannian manifolds [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. First, let us explain an important related problem called the Electrical Impedance Tomography (EIT) problem and note that it is equivalent to the classical Calderón problem in dimension \(n=3\) . Let \(M\)  be a body free of interior charges and made from a (possibly anisotropic) Ohmic material with conductivity \(\gamma \) . Applying a voltage \(\phi \)  on the boundary \(\partial M\)  induces a voltage \(u\)  in the interior and since the interior is free of charges, \(u\)  satisfies \(\mathrm {div}(\gamma ~ \mathrm {grad}(u))=0\) . We are not allowed access to the interior, which leaves us solely with the ability to making measurements along the boundary \(\partial M\) . Given \(\phi \) , we can measure the corresponding current flux \(\frac{\partial u}{\partial }\)  on \(\partial M\)  where \(\)  is the outward normal field. Hence, we have a map \(\Lambda \)  called the voltage-to-current map defined by \(\Lambda \phi \frac{\partial u}{\partial }\) . Is it possible to determine the conductivity \(\gamma \)  from the voltage-to-current map \(\Lambda \) ?
